Univariate Normal Distribution
Maximum likelihood estimation of the two parameters of a univariate normal distribution.
uninormal(lmean = "identitylink", lsd = "loglink", lvar = "loglink",
var.arg = FALSE, imethod = 1, isd = NULL, parallel = FALSE,
smallno = 1e-05, zero = if (var.arg) "var" else "sd")lmean, lsd, lvar |
Link functions applied to the mean and standard deviation/variance.
See |
var.arg |
Logical.
If |
smallno |
Numeric, positive but close to 0.
Used specifically for quasi-variances; if the link for the
mean is |
imethod, parallel, isd, zero |
See |
This fits a linear model (LM) as the first linear/additive predictor. So, by default, this is just the mean. By default, the log of the standard deviation is the second linear/additive predictor. The Fisher information matrix is diagonal. This VGAM family function can handle multiple responses.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
gaussianff() was deprecated but has been brought back
into VGAM nominally.
It should be called Mickey Mouse.
It gives a warning and calls
uninormal
instead
(hopefully all the arguments should pass in correctly).
Users should avoid calling gaussianff();
use glm with
gaussian instead.
It is dangerous to treat what is an
uninormal fit as a
gaussianff() object.
Yet to do: allow an argument such as eq.sd that enables
the standard devations to be the same.
Also, this function used to be called normal1() too,
but it has been decommissioned.
T. W. Yee
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.
udata <- data.frame(x2 = rnorm(nn <- 200))
udata <- transform(udata,
y1 = rnorm(nn, m = 1 - 3*x2, sd = exp(1 + 0.2*x2)),
y2a = rnorm(nn, m = 1 + 2*x2, sd = exp(1 + 2.0*x2)^0.5),
y2b = rnorm(nn, m = 1 + 2*x2, sd = exp(1 + 2.0*x2)^0.5))
fit1 <- vglm(y1 ~ x2, uninormal(zero = NULL), data = udata, trace = TRUE)
coef(fit1, matrix = TRUE)
fit2 <- vglm(cbind(y2a, y2b) ~ x2, data = udata, trace = TRUE,
uninormal(var = TRUE, parallel = TRUE ~ x2,
zero = NULL))
coef(fit2, matrix = TRUE)
# Generate data from N(mu = theta = 10, sigma = theta) and estimate theta.
theta <- 10
udata <- data.frame(y3 = rnorm(100, m = theta, sd = theta))
fit3a <- vglm(y3 ~ 1, uninormal(lsd = "identitylink"), data = udata,
constraints = list("(Intercept)" = rbind(1, 1)))
fit3b <- vglm(y3 ~ 1, uninormal(lsd = "identitylink", parallel = TRUE ~ 1,
zero = NULL), data = udata)
coef(fit3a, matrix = TRUE)
coef(fit3b, matrix = TRUE) # Same as fit3aPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.